Intertemporal consumption: myopic vs forward-

The consumption component of the model describes the behaviour of a representative household that makes consumption decisions over time and at each period in time. The models offer the possibility of considering the intertemporal consumption behaviour of ‘myopic’ or ‘forward looking’, perfect foresight households.

Myopic intertemporal consumption decisions are based on the

follow-3The basic structure of the CGE model in its non-energy version is largely based on Lecca et al. (2013). Although this thesis is meant to be self-contained, the reader can also refer to this work for further discussion about the model’s characteristics.

ing conventional consumption function:

Ct= Yt−St−HT AXt−CT AXt (2.1)

In (2.1) total consumption C is a equal to income Y minus savings S, income taxes HT AX and direct taxes on consumption CT AX. t is a subscript for a period of time, which is considered to be one year, given that the underlying data are annual. Any changes in income, savings or taxes are therefore reflected in each year’s consumption decision. House-holds’ income includes capital income KY and labour income LY , plus any transfer from Government and other institutions.

KYt= dsrk,h

In (2.2), capital income is described as the sum across sectors of cap-ital demand KD times rent of capcap-ital rk and where dsrk,h is the share of capital income that goes to households and it is calibrated from the SAM.⁴ Similarly, in (2.3) labour income is given by the share of labour income that goes to households dsrl,h times the sum of labour demand LD across sectors times the wage w. Households’ income also includes transfers from the government and other institutions.

The myopic specification lacks any expectations of future intertem-poral consumption decisions (Devarajan and Go, 1998; Go, 1994; Lecca

4Capital and Labour income are distributed among domestic institutions, such as households, government and firms.

et al., 2013; Partridge and Rickman, 2010). To accommodate future expectations we have the possibility of assuming that households have perfect foresight forward looking behaviour. The forward looking con-sumption model describes the behaviour of a representative household who seeks to maximise utility across time, subject to a budget constraint.

U^t(ct, . . . , cT) =

In equation (2.4) U is the intertemporal utility function, c is con-sumption at each time period t, ρ is the time discount factor and σ is the constant elasticity of marginal utility. The budget constraint states that at each period in time the change in total wealth W is a function of income, plus returns on wealth, minus consumption times the price of consumption P c.

Households’ wealth is composed of financial wealth (F W ) and non-financial wealth (N F W ) so that the following identity holds:

Wt= N F Wt+ F Wt (2.5)

The non-financial wealth includes wealth from labour income. It ac-cumulates as follows:

N F Wt(1 + r) = N F Wt+1+ Y Lt+X

ins

T RSins,t (2.6)

Equation (2.6) indicates that the compound value of today’s non-financial wealth is equal to tomorrow’s wealth plus net labour income Y L,

plus transfer from other institutions ins, such as firms and government, T RS. The financial wealth accumulation can be expressed as follows:

F Wt(1 + r) = F Wt+1+ KYt−St (2.7) Equation (2.7) states that current compounded wealth is equal to future period’s financial wealth, plus net income from capital KY minus savings S. The saving rate is exogenous and can be expressed as a share of income.

St= mps · Yt (2.8)

where mps is the marginal propensity to save and it is a parameter calibrated from the SAM, while Y is total income and it is equal in equilibrium to the discounted sum of financial wealth plus non-financial wealth. The solution of the utility maximisation intertemporal problem gives the Euler equation describing the optimal path of consumption across time.

Ct

Ct+1

=

 P ct·(1 + ρ) P ct+1·(1 + r)

⁻¹_σ

(2.9) According to (2.9) with fixed exogenous interest rate r⁵ the present discounted value of future consumption depends on future consumption prices. The parameter σ can be interpreted as the elasticity of intertem-poral substitution, measuring how easily household substitute current consumption for future consumption. This is set to 1.5 (Lecca et al.,

5I assume a fixed world interest rate equal to 0.04% (Lecca et al., 2013).

2014b).

In a steady state equilibrium, the present value of wealth is equal to the discounted sum of net income, which implies that the myopic and forward looking behaviour produces the same equilibrium results.

However, the short-run equilibrium and the adjustment paths in response to any disturbance to the economy differ between the two models (Lecca et al., 2013).

In this thesis I assume forward looking consumption behaviour in Chapter 3, in order to ensure consistency with the analysis of the na-tional case study of the UK conducted by Lecca et al. (2014a). In this way, differences in results are purely driven by the regional nature of Scotland, reflected in the different dataset and in the assumption of in-terregional migration of workers. In Chapter 4, I assume that households are myopic. It can be argued that there is some degree of myopia in households’ consumption behaviour. Therefore, the assumption of in-tertemporal perfect foresight, household maximising behaviour can be regarded as a limiting case that may not be a good representation of real consumption behaviour. Additionally, the analysis in Chapter 4 is focussed on the lowest income households, whose ability to optimise their lifetime income is significantly circumscribed by their dependence on transfers from government and other types of transfers. Ideally, I could have assumed that some groups are myopic and some other are forward-looking or some other type of behaviour.⁶ However, in the con-text of Chapter 4 this would have gone beyond the main objective of the paper which is to investigate the implications of energy efficiency on

6In fact, it is straightforward to set the model to reflect this type of assumption.

lower income households. Finally, in Chapter 5, I focus on long-run equi-librium results, and therefore I utilise for simplicity the myopic model given that the results are the same for this specific equilibrium solution.